证明：设数列{an},an=1/n(n+1)(n+2),则an=1/2{[1/n-1/(n+1)]-[(1/n+1)-1/(n+2)]},得1/1*2*3+1/2*3*4+.+1/n(n+1)(n+2)=a1+a2+……+an=1/2[(1-1/2)-(1/2-1/3)]+1/2[(1/2-1/3)-(1/3-1/4)]+……+1/2{[1/n-1/(n+1)]-[(1/n...